According tothe Pew poll, Paul would siphon off significant support from Romney among Republican-leaning independent voters and the most conservative Republicans. More than two-thirds of Paul’s support would come from Romney.

Romney, in a head-to-head match-up with Obama, trails by 5 percentage points, 50 percent to 45 percent. But with Paul in the mix, Obama’s lead balloons to 12 points — 44 percent to 32 percent. Paul draws 18 percent in that theoretical contest, close to the 19 percent won by fellow Texan Ross Perot in his 1992 third-party bid.

Paul has repeatedly declared that he is not currently weighing a third-party candidacy. But he hasn’t definitively ruled out that possibility.

The Pew poll shows Romney leading the rest of the GOP field by a wide margin: 31 percent, to 16 percent for Newt Gingrich and 15 percent for Paul. But only 33 percent of all American voters have a positive impression of Romney, while 47 percent hold a negative view of the GOP frontrunner.